opponent has 67% check raise frequency. should i have given up that hand or called and barrelled the turn again? i dont believe he has better holdings. however it was likely that he was going to barrel the turn after the check raise.

If that is over a decent sample, I would check behind and hope to hit one of your backdoor draws or a pair. The point of making a cbet here is to make BB fold his air and underpair/bottom pair. You want him to fold air since it usually has around 6 outs and it's hard to get to showdown if he bets. If his check/raise frequency is so high, he is playing his air aggressively, so the value of making a cbet is diminished in a situation where it's hard to play back (this one). Combined with the fact that you have showdown value and can hit good turn cards, I think checking is better.

Bad board to be c-betting on... it's somewhat connected, T high and has a flush draw. He not folding any flush or straight draws here for sure. He's not folding Tx, he ain't folding any pocket pair...

The only hands you're folding out here are broadway pretty much... so check behind and hope for a good turn card. Any spade en most jack or 7 turns will significantly improve the equity of your hand.

As played you have to fold vs his check/raise, eventhou it's a small check/raise I wouldn't go nuts on this board as he could very easily have a flush draw with overcards and if that's the case he's never folding here any more.

you get attacked sometimes that board
if you afraid that he might c/r then check back flop, call turn and decide on the river
I think 3-bet bluff or float here is not the best idea, since he would shove his draws and likely would barrel any turn card if you call